Note that when two lines have slopes of m₁ and m₂, then
(i) If m₁ = m₂, then the lines are parallel.
(ii) If m₁*m₂ = -1, then the lines are perpendicular.
Let us evaluate the given lines.
a. y = 4x - 1 and 12x = 3y + 7
y = 4x - 1 => m₁ = 4
Write the second equation in standard form.
3y = 12x - 7
y = 4x - 7/3 => m₂ = 4.
m₁ = m₂.
Answer: PARALLEL
b. x - 7y = 10 and 2x + 14y = 21
In standard form,
7y = x - 10 or y = (1/7)x - 10/7 => m₁ = 1/7
14y = - 2x + 21 or y = -1/7 + 3/2 => m₂ = -1/7
m₁ ≠ m₂ and m₁*m₂ ≠ -1.
Answer: NEITHER
c. 5x + 6y = 18 and 18x - 15y = 36
In standard form,
6y = -5x + 18 or y = -(5/6)x + 3 => m₁ = -5/6
15y = 18x - 36 or y = (6/5)x - 12/5 => m₂ = 6/5
m₁*m₂ = -1
Answer: PERPENDICULAR
d. x =1 and y = 1
x = 1 => m₁ is undefined
y = 1 => m₂ = 0
m₁ ≠ m₂ and m₁*m₂ ≠ -1
Answer: NEITHER
Consecutive even integers..x, x + 2, x + 4
x + (x + 2) + (x + 4) = 6216
3x + 6 = 6216
3x = 6216 - 6
3x = 6210
x = 6210/3
x = 2070
x + 2 = 2070 + 2 = 2072
x + 4 = 2070 + 4 = 2074 <===house 3
Answer:
your answer is 1!
The gcf of 7 and 9 is the largest positive integer that divides the numbers 7 and 9 without a remainder. Spelled out, it is the greatest common factor of 7 and 9. Here you can find the gcf of 7 and 9, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the gcf of 7 and 9, but also that of three or more integers including seven and nine for example. Keep reading to learn everything about the gcf (7,9) and the terms related to it.
What is the GCF of 7 and 9
If you just want to know what is the greatest common factor of 7 and 9, it is 1. Usually, this is written as
gcf(7,9) = 1
The factors of 9 are 9, 3, 1.
The factors of 7 are 7, 1.
The common factors of 9 and 7 are 1, intersecting the two sets above.
In the intersection factors of 9 ∩ factors of 7 the greatest element is 1.
Therefore, the greatest common factor of 9 and 7 is 1.
